A Mechanistic Model for the Two-Phase Slug Flow of the Purely Viscous Non-Newtonian Liquids through Pipes

Abstract

Mechanistic slug models generally depend on several empirical correlations. This work presents an extended model, which incorporates a recently theoretically developed family of friction equations for purely viscous non-Newtonian fluids to reduce this dependency. In contrast to other models where a fixed transition Reynolds number is used, a proper rheology-dependent laminar-to-turbulent transition criteria has been adopted. Finally, to fully specify the characteristics of the slug flow, a new model is introduced for the slug frequency, by balancing the pressure forces and the drag over the gas bubble. The resulting model requires just one empirical coefficient, drag coefficient of the bubble, which depends on the rheology of the fluids and diameter of the pipe. The developed models have been extensively verified with the experimental data, for the two-phase flows with Newtonian and non-Newtonian (power law and Bingham) liquid phase. Our mechanistic model predicts the pressure drop of the experimental data within ±20% error range, while it does not introduce any new empirical coefficient for the non-Newtonian case. This model, besides its simplicity and accuracy, successfully captures the physical trends in experimental data where other available models fail. The frequency model with calibrated drag coefficient reproduces the experiments with less than 30% error, while one can find a universal drag coefficient which can reproduce most of the experimental observations within the same error range. To summarize, the proposed models can fully characterize two-phase slug flows in presence of a non-Newtonian purely viscous fluid phase.